Relativistic Lorentz force
= Relativistic Lorentz force
$m\,du^\mu/d\tau=qF^\mu{}_\nu u^\nu$ gives $d\mathbf p/dt=q(\mathbf E+\mathbf v\times\mathbf B)$ and $d(\gamma mc^2)/dt=q\mathbf E\cdot\mathbf v$.
= Relativistic Lorentz force
$m\,du^\mu/d\tau=qF^\mu{}_\nu u^\nu$ gives $d\mathbf p/dt=q(\mathbf E+\mathbf v\times\mathbf B)$ and $d(\gamma mc^2)/dt=q\mathbf E\cdot\mathbf v$.